complexity and economics - ufpr · class01-complexity class02-economicsreferenciasˆ oppening...

Complexity and EconomicsThe lowest simplicity you can achieve is the complexity

Joao Basilio [email protected]

Department of EconomicsGraduate Program in Economic Development

Curitiba-Parana-Brazil

13 de junho de 2016

Class01-Complexity Class02-Economics Referencias

Complexity and Economics

Lecture 01

Complexity in General Science

“Man has been impelled to scientific inquiry by wonder and by need.Of these wonder has been incomparably more fertile.”

Hayek, 1967, p. 22

Complexity and Economics 13 de junho de 2016 2 / 39


Oppening

Economics and Complexity is an introductory course for researchers and graduatedstudents of economy who wish to comprehend the complex approach applied ineconomics and learn how to build agent based models. The curse aims to introduceontological concepts and definitions, set out examples of what is a complex system andhow these systems works and evolve in time. In a more pragmatic way the course aimsto introduce two specific tools used to build up economic agent based models: theLaboratory of Simulation and Development (LSD) and Netlogo. Some economic andsocial models will be built by using computational resources intensively . Massiveattention will be spent in theoretical questions in economics and programming methodsand activities applied to the development of agent-based models (ABM).



Complexity - Motivations (Science with a pinch of emotion)

I think the next century will be the century of complexity.Stephen Hawking - January 2000



Complexity - Motivations (Science with a pinch of emotion)

Science has explored the microcosmos and the macrocosmos; we have a good sense of the lay of the land.The great unexplored frontier is complexity

Heinz-Pagels: The Dreams of Reason

Economic science has explored the microeconomics and the macroeconomics; we have a (not so) goodsense of the economic system. The great unexplored frontier is complexity

Basilio, this economic course



Why economists do not understand Complexity well, if so?

Our brains were designed to understand hunting and gathering, mating and child-rearing: aworld of medium-sized objects moving in three dimensions at moderate speeds.

Dawkins (1987) in The Blind Watchmaker



Frozen view?

“Economic is not a evolutionary science - by the confession of its spokesman: and theeconomists turn their eyes with something of envy and some sense of baffled emulation to thesesrivals that make broad their phylacteries [phylum] with the legend, ‘up to date’.

Precisely wherein the social and political sciences, including economics, fall short of beingevolutionary sciences, is not so plain. ”

Veblen (1899, p. 374-5)

“The same reasoning applies today to the Complexity Theory context. Agents thus live in aworld where their beliefs and strategies are constantly being ‘tested’ for survival within anoutcome or ‘ecology’ these beliefs and strategies together create. Economics has largelyavoided this non equilibrium view in the past, but if we allow it, we see patterns or phenomenanot visible to equilibrium analysis.”

Arthur (2013)



Reductionism and Complexity

Reductionism is the most natural thing in the world to grasp. It’s simply the belief that “a wholecan de understood completely if you understand its parts, and the nature of their ‘sum’ ”. Noone in her left brain could reject reductionism.

Hofstadter (1979, p. 318)

The scientific method: “To dive all the difficulties under examination into as many parts aspossible, and as many as were required to solve then” and “to conduct my thoughts in a giveorder, beginning with the simplest and most easily understood objects, and gradually ascending,as it were step by step, to the knowledge of the most complex”

Descartes (1637)



Why Complexity

• Many phenomena in the physic, natural and social dimension of the reality can notbe explained with concepts of mechanical physic

• Large structures are assembled from particles or individuals in a way far beyondthat the simple aggregation and sum

• Structures evolves to an unpredictable future and forms• The time arrow is not reversible and many traditional scientific methods fails to

explain and forecast• Commonly the systems shows up heterogeneity and produces novelty• The system (societies) are populated by ± heterogeneous agent who interacts

with the others• We are far from comprehend the World or the Reality with the newtonian machine

or statistical viewpoint, mainly in social and economic science

• Deterministic x Statistical x Complexity view of the world

Despite the progress of science in the XX century, many questions and answersremains open and can not be thought with traditional viewpoint



From simple description of regularities to emergent properties

Knowledge:• By deduction starting with intuition• By induction observing data with statistical lens and ending with some intuition too• By interactions playing - the evolutionary science with many agents living in and

generating many worlds (Epstein, 2006, Generative Social Science)

The advance of science will thus have to proceed in two different directions : while it iscertainly desirable to make our theories as falsifiable as possible, we must also push forward

into fields where, as we advance, the degree of falsifiability necessarily decreases. This is theprice we have to pay for an advance into the field of complex phenomena.

Hayek (1967, p. 29)



So, what is complexity?

An interdisciplinary field of research that seeks to explain how large number of relatively simple entitiesorganize themselves, without the benefit of any central controller into a collective whole that createspatterns, uses information, and, in some cases, evolves and learns.

Mitchell (2009, p.4)

Complex systems consist of units interacting in a hierarchy of levels, including subsystems composed ofeven more intricate sub-subsystems.

Complex systems exhibit emergent properties due to the interaction of their subsystems when certainunspecific environmental conditions are met, and they show temporal and/or spatial patterns on a scalethat is orders of magnitude bigger than the scale on which the subsystems interact.

Fuchs (2013, p.4)

A complex thing is something whose constituent parts are arranged in a way that is unlikely to have arisenby chance alone.

Dawkins (1987, p.7)



So, what is complexity?

A system of connected agents that exhibits an emergent global behavior not imposed by a centralcontroller, but resulting from the interactions between agents.

Boccara (2004, p.4)

The science of complexity suggests that while life is in accordance with the laws of physics, physics cannotpredict life.

Erdi (2008, p.5)

Complexity results from the inter-relationship, inter-action and inter-connectivity of elements within asystem and between a system and its environment. Murray Gell-Mann, in Complexity Vol. 1, No. 5,1995/96, traces the meaning of complexity to the root of the word. Plexus means braided or entwined, fromwhich is derived complexus meaning braided together, and the English word “complex” is derived fromthe Latin. Complexity is therefore associated with the intricate inter-twining or inter-connectivity ofelements within a system and between a system and its environment.

Chan (2001)



Ants, Neurons, Crowd and other complex system



Complexity Approaches

Important concepts

• Diversity/variety• High Non-linearity• Hierarchy• Non-Predictability• Interactions (at micro and macro

level)• Network• Self organization• Adaptive system• Emergence• Learning and information

computation• Evolution



Complexity Approaches

• Non-linear system of differential equations (at macro level)• Instability• Multiple equilibrium• Dynamic replicator or Lotka-Voltera system• Bifurcation• Deterministic Chaos• Fractal structures

• Agent-based models with interactions• Genetic Algorithms/Evolutionary Computation• Cellular Automata• Networks• Spatially Oriented models (e.g. using Netlogo)• Micro-macro models in difference (e.g. using LSD in economic models)

• Evolution, Adaptive System and Computation• Computation of information• Individual change• Structural change• Path-dependence and cumulative causation (Myrdal)• Auto-organization (from chaos to order)



Dynamic process

Four way to represent dynamics

• Equilibrium• Cycle• Random• Complexity



Non-linear system of differential equation

Figura: Thomas Malthus - 1766-1839

The malthusian exponenctial equation is (Malthus, 1798)

dN(t)dt

= rN(t) −→ N(t) = N(0)ert

It is a one dimensional equation



Non-linear system of 1 differential equation

Figura: Pierre Francois Verhulst - 1804-1849

The logistic equation was coined by Verhulst (1838)

dN(t)dt

= rN(t)(

1− N(t)K

)−→ N(t) =

K1 + CKe−rt

where C = 1N(0) −

1K is the constant of integration and initial condition. It is a one

dimensional quadratic equation and K is the carry capacity.




Logistic function: from linear behavior to deterministic chaos

dN(t)dt

= rN(t)(

1− N(t)K

)

The period doubling route to chaos




The van der Pol (1926) model

x(t) = y(t)

y(t) = α(

1− x(t)2)

y(t)− x(t)

Phase Diagram

View it in Maple...




The Lorenz (1963) Attractor model

x(t) = σ (y(t)− x(t))

y(t) = x(t) (−ρ− z(t))− y(t)

z(t) = −βz(t) + x(t)y(t)

Mostrar modelo no Maple... and on the Wikipedia:http://en.wikipedia.org/wiki/Lorenz_system


http://en.wikipedia.org/wiki/Lorenz_system


Agent-based models with interactions

All the preceding examples were based in evolution of agregated, summed up oraverage quantities. No heteregeneity or interactions was present. In theAgent-based-world, the behavior of an agents have an effect on the others, andindividual following a simple and particular rule, can produce surprising aggregatedeffects. Stem cell can divide yourself and generate diferent organs. One initial cellgenerate a complete and different body within the same species. Individuals followinghis particular or collective simple rule generate a social or economic reality, observedand analysed by the traditional methodos: econometrics and structural models. The

aggregated researcher can not answer suitably the question: Where does thisaggregated pattern cames from?

In order to answer this you need a agent-based-world (model) inhabited byheterogeneous agents more than representative one.




Cellular Automata-CAAt a very general level, one might say that computation is what a complex system doeswith information in order to succeed or adapt in its enviromnet. Mitchell (2009, cap. 10,p. 146)

The CA is a kind of complex system where the agents (cell) can change its status ormove to another place according to a set of disposal simple rule and depending of thestatus of its neighborhood. The CA generaly is represented in a Lattice (grid) of cells.

Game of Life (Conway) and Wolfram Cellular Automata




Game of Life rule

Denoting on cells as alive and off cells as dead, Conway defined the rule in terms offour life processes:• Birth, a dead cell with exactly three live neighbors becomes alive at the next time

step;• Survival, a live cell with exactly two or three live neighbors stays alive;• Loneliness, a live cell with fewer than two neighbors dies• Dead, a dead cell with fewer than three neighbors stays dead



Evolution, Adaptive System and Computation

Evolution has been processed by computation. How the evolution process manipulates theinformation? Dawkins (1987): by a Blinded Watchmaker. Evolution goes on by small andlocated random mutation towards a long and slow and cumulative selection.

Consider a system composed by “n” constituents (agents) or a space-state with “n”configuration who or which presents only two characteristics or attribute a = {0, 1} whichcan means black and white, optimistic and pessimistic, altruist or selfish, or anything else. Ifwe arrange this “n” components in a one-dimensional sequence we get an array or alandscape with many different results or configuration at instant t :

N=2 N=3A={0, 0}, {0, 1}, {1, 0}, {1, 1} A={0, 0, 0}, {0, 0, 1}, . . . , {1, 1, 1}A = 22 = 4 A = 23 = 8N=100A = 2100 = 1.267.650.600.228.229.401.496.703.205.376 = 1, 267E30

The size of Universe: 1.2 to 3.0E1023 stars→ 1078 to 1082 atoms



Agent-Based Models

Exemplos no Netlogo1. Computer Science/Cellular Automata/Life (Game of Life)2. Social Science/El Farol3. Social Science/SugarSpace34. Sbicca & Pereima (2014)5. Einloft & Pereima (2016)

Exemplos no LSD1. Brian Arthur2. Nelson & Winter3. Higachi & Pereima (2015)4. Pereima & Gabardo (2016)



Complexity and Economics

Lecture 02

Complexity in Economic Science



Why Complexity: An example with technology

Representative x Heterogeneous Agents• In the representative agents world the whole is the sum of the parts

Yi = Fi(Ai ,Ki , Li)

Y =

∫ n

0Yidi or Y =

∫ U(x,i)

L(x,i)Yidi

• In the heterogeneous agents world the interactions between the same agentsproduce different patterns in the macro level, some of them astonishing



Example with technology



Type of complexity in Economics



Level of Interactions

In economics, the agents can interact at different and simultaneous level

• Micro-Micro level• Consumer-to-Consumer (collective behaviour - ex: bandwagon effects)• Firm-to-Firm (price and technological competition)• Consumer-to-Firm (consumer choose the firm)

• Micro-Macro level• This is the case when agents monitor an aggregated variable.



Complexity and Microfoundations

What kind of microfoundations (Cimoli and Porcile, 2015)?

• Optimization - Fully Rational: can be achieved by deterministic or probabilisticuncertainty. High (infinite) computation capacity + access to informationor

• Rule based: learning adaptive, habits, heuristics, memory.



Threshold Model of Collective Behavior

Individual Preferences, Interactions and Emergence of Aggregated Outcomes

“Because sociological theory tend to explain behavior by institutionalized norms and values, thestudy of behavior inexplicable in this way occupies a peripherical position in systematic theory.Work in the subfields which embody this concern - deviance for individuals and collectivebehavior for groups - often consists of attempts to show what prevent the stablished patternsfrom exerting their usual sway. In the field of collective behavior, one such effort involves theassertion that new norms or beliefs ‘emerge’ in situations where old ones fail or few precedentsexist.Such arguments are an advance over crude psychologizing about crowds’ stripping away the’veneer’ of civilization from their participants. But I will argue here that knowing the norms,preferences, motives, and beliefs of participants in collective behavior can in most cases, onlyprovide a necessary but not sufficient condition for the explanation of outcomes; in addition oneneeds a model of how these individual preferences interact and aggregate.”

Granovetter (1978, p. 1420-21)

see more: Granovetter



Interacting Agents

An example of interaction in a social model:

See: Netlogo, Social Sciences - Altruism ModelEinloft & Pereima (2016)



Interacting Agents

An example of interaction in a economic model with Brian Arthur



Interacting Agents

An example of interaction in a economic model:

See: LSD-Higachi & Pereima (2016)



References I

Arthur, W. B. (2013). Complex economics: A different framework for economic thinking. SFI WorkingPaper, (2013-040-12).

Boccara, N. (2004). Modeling Complex Systems. Springer Verlag New York Inc, USA.Chan, S. (2001). Complex adaptative systems. Mimeo. ESD.83 Research Seminar in Engineering Systems.Cimoli, M. and Porcile, G. (2015). what kind of microfoundations: Notes on the evolutionary approach.

Series: Production Development, 198.Dawkins, R. (1987). The Blind Watchmaker: Why the evidence of evolution reveals a universe without

design. W. W. Norton & Company Inc., New York, USA. Reprinted edition 1996.Descartes, R. (1637). Discourse on the method. Oxford University Press, London. Oxford World’s Classic,

printed in 2006.Epstein, J. M. (2006). Generative Social Science: Studies in agent-based computacional modeling.

Princeton University Press, Princeton, New Jersey, EUA.Erdi, P. (2008). Complexity Explained. Springer-Verlag, Berlin Heidelberg.Fuchs, A. (2013). Nonlinear Dynamics in Complex System: Theory and Appliations for the Life, Neuro, and

Natural Sciences. Springer-Verlag, Berlin.Granovetter, M. (1978). Threshold model of collective behavior. The American Journal of Sociology,

83(6):1420–1443.Hayek, F. A. (1967). Studies in Philosophy, Politics and Economics. The University of Chicago Press,

Chicago.Hofstadter, D. R. (1979). Godel, Escher, Bach: an Eternal Golden Braid. Basic Book, New York.



References II

Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2):130–141.

Malthus, T. (1798). An Essay on the Principle of Population. John Murray, London, 6th edition. 1826.

Mitchell, M. (2009). Complexity: a Guide Tour. Oxford University Press, Oxford, USA.

van der Pol, B. (1926). On relaxation-oscillations. Philosophical Magazine and Journal of Science, 2(7).

Veblen, T. (1899). A Teoria da Classe Ociosa: Um Estudo Estudo Economico das Instituicoes. AbrilCultural, colecao Os Economistas, Trad. portugues 1983, Sao Paulo.

Verhulst, P. F. (1838). Notice sur la loi que la population poursuit dans son accroissemen. Correspondancemathematique et physique, 10:113–121.


complexity and economics - ufpr · class01-complexity class02-economicsreferenciasˆ oppening...

Documents